Clifford Boundary Conditions : A Simple Direct-Sum Evaluation of Madelung Constants
We propose a simple direct-sum method for the efficient evaluation of lattice sums in periodic solids. It consists of two main principles: (i) the creation of a supercell that has the topology of a Clifford torus, which is a flat, finite, and borderless manifold; (ii) the renormalization of the distance between two points on the Clifford torus by defining it as the Euclidean distance in the embedding space of the Clifford torus. Our approach does not require any integral transformations nor any renormalization of the charges. We illustrate our approach by applying it to the calculation of the Madelung constants of ionic crystals. We show that the convergence toward the system of infinite size is monotonic, which allows for a straightforward extrapolation of the Madelung constant. We are able to recover the Madelung constants with a remarkable accuracy, and at an almost negligible computational cost, i.e., a few seconds on a laptop computer.
| Medienart: |
E-Artikel |
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| Erscheinungsjahr: |
2020 |
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| Erschienen: |
2020 |
| Enthalten in: |
Zur Gesamtaufnahme - volume:11 |
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| Enthalten in: |
The journal of physical chemistry letters - 11(2020), 17 vom: 03. Sept., Seite 7090-7095 |
| Sprache: |
Englisch |
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| Beteiligte Personen: |
Tavernier, Nicolas [VerfasserIn] |
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| Anmerkungen: |
Date Revised 03.09.2020 published: Print-Electronic Citation Status PubMed-not-MEDLINE |
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| doi: |
10.1021/acs.jpclett.0c01684 |
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| funding: |
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| Förderinstitution / Projekttitel: |
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| PPN (Katalog-ID): |
NLM313620679 |
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| 100 | 1 | |a Tavernier, Nicolas |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Clifford Boundary Conditions |b A Simple Direct-Sum Evaluation of Madelung Constants |
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| 500 | |a Date Revised 03.09.2020 | ||
| 500 | |a published: Print-Electronic | ||
| 500 | |a Citation Status PubMed-not-MEDLINE | ||
| 520 | |a We propose a simple direct-sum method for the efficient evaluation of lattice sums in periodic solids. It consists of two main principles: (i) the creation of a supercell that has the topology of a Clifford torus, which is a flat, finite, and borderless manifold; (ii) the renormalization of the distance between two points on the Clifford torus by defining it as the Euclidean distance in the embedding space of the Clifford torus. Our approach does not require any integral transformations nor any renormalization of the charges. We illustrate our approach by applying it to the calculation of the Madelung constants of ionic crystals. We show that the convergence toward the system of infinite size is monotonic, which allows for a straightforward extrapolation of the Madelung constant. We are able to recover the Madelung constants with a remarkable accuracy, and at an almost negligible computational cost, i.e., a few seconds on a laptop computer | ||
| 650 | 4 | |a Journal Article | |
| 700 | 1 | |a Bendazzoli, Gian Luigi |e verfasserin |4 aut | |
| 700 | 1 | |a Brumas, Véronique |e verfasserin |4 aut | |
| 700 | 1 | |a Evangelisti, Stefano |e verfasserin |4 aut | |
| 700 | 1 | |a Berger, J A |e verfasserin |4 aut | |
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| 773 | 1 | 8 | |g volume:11 |g year:2020 |g number:17 |g day:03 |g month:09 |g pages:7090-7095 |
| 856 | 4 | 0 | |u http://dx.doi.org/10.1021/acs.jpclett.0c01684 |3 Volltext |
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